Chajda, Ivan Regularity and permutability via transferability of tolerances. (English) Zbl 0957.08001 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 35, 39-42 (1996). Summary: An algebra \(A\) has \(n\)-transferable tolerances if for any \(a,b,c\in A\) there exist \(d_1,..., d_n \in A\) such that \(T(a,b)= T(c,d_1)\vee \dots\vee T(c,d_n)\) in the tolerance lattice \(\operatorname {Tol}A\). We prove that a variety \({\mathcal V}\) is regular and permutable if and only if each \(A\in{\mathcal V}\) has \(n\)-transferable tolerances. Analogously we characterize varieties of 0-regular and permutable congruences. MSC: 08A30 Subalgebras, congruence relations 08B05 Equational logic, Mal’tsev conditions Keywords:0-regularity; permutability of congruences; regular variety; permutable variety; \(n\)-transferable tolerances; tolerance lattice × Cite Format Result Cite Review PDF Full Text: EuDML References: [1] Chajda I.: A Maľcev characterization of tolerance regularity. Acta Sci. Math. (Szeged), 42 (1980), 229-232. · Zbl 0454.08003 [2] Chajda I.: Transferable tolerances and weakly tolerance regular lattices. Colloq. Math. Soc. J. Bolyai 43., Universal Algebra, Szeged 1983, North-Holland 1985, 27-40. [3] Chajda I.: Algebraic Theory of Tolerance Relations. Monograph Series of Palacký University, Olomouc, 1991, 117 p. · Zbl 0747.08001 [4] Duda J.: Maľcev conditions for regular and weakly regular subalgebras of the square. Acta Sci. Math. (Szeged), 46 (1983), 29-34. [5] Werner H.: A Maľcev conditions for admissible relations. Algebra Univ. 3 (1973), 263. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.